# Final Exam

### **Question 1** (20 pts)

What is a rounding error? Please write a program to show the rounding error occurs. 

*(Essay / Open Answer)*

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### **Question 2** (20 pts)

Here is the linear equations that we want to solve:

$$
\begin{aligned}
3x_1 + 5x_2 - 3x_3 &= 10 \\
4x_2 + 4x_3 &= -5 \\
2x_1 - 9x_2 + 6x_3 &= 13
\end{aligned}
$$
 
1. Please show the **Gauss Elimination method** matrix based on the above equation, you do NOT need to solve x1, x2, x3; just show the matrix that we will use to solve the problem.
2. Write the Python code to solve the system shown above. You can use **any** one of the methods studied in the book. 

*(Essay / Open Answer)*

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### **Question 3** (20 pts)

Find the linear interpolation at x = 3 based on the data x = [2, 5, 6] and y = [2, 3, 1]. 

*(Essay / Open Answer)*

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### **Question 4** (20 pts)

Write a Python code to find an approximated root of the function $f(x) = x^2 + 3x + 1$, starting with $x=10$

*(Essay / Open Answer)*

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### **Question 5** (20 pts)

Find all 2-item-set association rules on the following figure based on:

- minimum support = 50%,
- minimum confidence = 70%,

(Show ALL required steps)

T1: BDE
T2: ABD
T3: BC
T4: ABD
T5: ABCD

*(Essay / Open Answer)*